Two things almost everyone knows about Susan Greenfield. She wears mini-skirts and she's a scientist. The problem for Greenfield is the order in which they are ranked, for her appearance often attracts bigger headlines than her work. There aren't that many women working in science in the first place, so when a woman scientist is as comfortable in the pages of Hello! as in a peer-reviewed journal, and has patented a look in designer rock-chick chic, then it's safe to assume that some kind of statement is being made.

So first things first. Yes, she is wearing a mini-skirt, yes, she is concerned about whether she should put on some lipstick for the photographs and, yes, she is looking just great anyway. Greenfield maintains that her appearance is separate to her identity as a scientist. "The most important thing is that I should remain true to myself," is a frequent refrain in our conversation and she affects a battle-hardened je ne regrette rien attitude towards everything in her past.

But you suspect it's not that straightforward. Greenfield is as savvy a media player as she is an academic, and you can't help feeling there's a conscious trade-off at work. If science is her passion, then popularising science is her grand passion and in a world that measures popularity by column inches, then pretty much anything goes. You can't fault the logic: you can't get your ideas across if nobody listens and if the easiest way to grab people's attention in the first place is on the strength of your appearance, then so be it. You might lose a few, you might look a prat now and again, but overall you'll be in profit.

It's a formula that has served her well so far. Aside from the day jobs as Fullerian professor of physiology at the department of pharmacology at Oxford, and director of the Royal Institution, she's picked up the Michael Faraday Medal from the Royal Society, a CBE and life-peerage from the present government, has written a report on women in science for Patricia Hewitt, and happily trots the globe in the democratisation of science.

Last summer she was in Adelaide as "speaker in residence" - the perfect job for someone who scarcely draws breath between sentences - and last month she was mixing it with the great and the good at the World Economic Forum in Davos. Apart from a round-robin email she received from the caring, sharing Sharon Stone, the biggest name she ran up against was Larry Summers, the president of Harvard, who was recently reported as saying that women were genetically incapable of good science.

On the way up in the lift to her office, Greenfield laughingly described Summers as "that toerag", but she is rather more measured once the tape is running. Though the underlying sentiment remains the same. "I was chairing a meeting on 'Gender and the Brain'," she says, "and it was only natural that Summers's comments were discussed. A colleague of his apologised on his behalf and asked if I would like to meet him later that week.

"We had a good conversation where he rather moderated the position he was reported to have taken. He admitted he was wrong to have spoken out on a subject on which he had no expertise, and I was able to point out that even if we could agree on what was meant by 'good at science' there was no gender-based, genetic bio-determinism involved. There are issues about why women are under-represented in science but these are best explained by socialising factors."

This encounter epitomises the pay-off for Greenfield. No matter how good a scientist she may be, there was not a cat in hell's chance of her getting a one-to-one with Summers so quickly, unless she had the requisite public profile and the media clout. But it does have its professional downsides. Last week, Greenfield was accused of dumbing down science by selling the rights to the Royal Institution's Christmas lectures to Channel 5 rather than offering them back to the BBC.

The tension between Greenfield and some of her peers has been going on for years and shows no sign of diminishing - not least because it's hard to fight a battle when your enemies refuse to identify themselves. Last year, two fellows were quoted as saying they would resign if Greenfield were elected to the Royal Society - just the latest in a long line of anonymous detractors.

"It's hard to engage with it all," she admits, "because you're never quite sure who or what you're dealing with. Everyone is always quite nice to me in person and then I hear I'm being criticised behind my back, though the criticisms are always fairly vague. Rather than explaining why and where my science is weak, they restrict themselves to general value statements with no evidence to back them up."

Just what Greenfield has done to upset so many people is hard to work out. Research on the brain and consciousness is generally regarded as rather left-field and does not attract large grants, so it can't be about the money. What's more, within the neuroscientific community, her views are fairly mainstream. There's no grand theory of consciousness, there's no grand design on creating artificial intelligence; just standard, uncontroversial scientific theory.

"We don't even know what questions we ought to be asking about consciousness," she points out, "let alone understand how it may be composed. So how can you build artificial intelligence if you don't know what to leave in or leave out? My understanding is that there are degrees of consciousness: a rat is less conscious than a foetus is less conscious than an adult - and an adult may be more or less conscious at different times of the day. This hypothesis means that you have a route to better understanding consciousness by measuring the network assembly of neurons in the brain."

Last month Greenfield won a £1m research grant from the US-based John Templeton Foundation to head the Oxford Centre for Science of the Mind - a multi-disciplinary team of academics from pharmacology, human anatomy, physiology, neuroscience, theology and philosophy. It's ground-breaking stuff, as it's the first time that science and the humanities have combined in this way and it's no coincidence that Greenfield has been one of its architects. If you're looking to award a grant in an obscure area, who better to give it to than a respected academic with a high media profile: that way you're guaranteed a public return for your cash.

It's equally in character that the centre's work has already been hyped out of all recognition, with lurid speculation about torturing religious zealots. Greenfield shrugs non-committally. "I'm used to the media getting things wrong," she says, "but I understand its agenda is to sell papers. The reality is rather more dull. Researchers will be applying a mildly uncomfortable chilli paste to volunteers to determine how people react to pain and what difference the power of belief might make."

As with much of Greenfield's work on Alzheimer's and Parkinson's, the research is large part blue-skies, big picture with a touch of the short-term practical thrown in. "Within two years we might be able to give some answers to what a belief means in brain terms - and how it can affect your immune system, but the longer-term question of how beliefs can change a subjective state will certainly take a great deal longer."

If, indeed, they are ever answered. Greenfield insists she only gets satisfaction from seeking answers to the big questions, but it's hard to resist the notion that there's something masochistic about working on problems to which you'll almost certainly never get a definite answer. People have spent thousands of years trying to make sense of consciousness and may well be not much further on several thousand years hence, and no one seriously believes a cure for Alzheimer's is anything but a distant dream.

Greenfield's willingness to continually put her head above the media parapet also verges on the masochistic. For if the problem isn't her science, then you have to conclude it's personal. Is it because she's a woman? Or because she's successful? Or because she's just a little bit too loud for some academics' liking? Or some combination of the three?

"I don't have the same scientific background as many of my peers," she says, "so perhaps my face doesn't quite fit. I studied classics at school, psychology as an undergraduate, and only switched to science as a postdoc. So there are huge gaps in my scientific training - [physics and chemistry are the two biggest casualties] - and I still have a great deal of sympathy with the media and politicians who like their science in black and white, rather than academics who prefer to restrict themselves to shades of grey. This doesn't mean you compromise the evidence: you just explain it clearly and simply."

This isn't something that many scientists are good at doing, which is why Greenfield has made it her life's work. "Only last week I got a letter from a schoolgirl saying, 'girls like me need women like you'," she says. And as my hour comes to an end, someone from Canadian radio is waiting outside in the corridor. The science sales show never ends.

The CV

Name: Susan Greenfield

Age: 54

Job: Fullerian professor of physiology, professor of pharmacology, Oxford University; director, Royal Institution of Great Britain

Other honours : Michael Faraday medal, 1998; honorary fellow of Royal College of Physicians, 1999; CBE, 2000; life peerage, 2001

Publications: Journey to the Centre of the Mind, 1995; Private Life of the Brain, 2000; 100 Things To Do Before You Die, 2004